162,155 research outputs found

    Bifurcations from families of periodic solutions in piecewise differential systems

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    Consider a differential system of the form x′=F0(t,x)+∑i=1kεiFi(t,x)+εk+1R(t,x,ε), x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon), where Fi:S1×D→RmF_i:\mathbb{S}^1 \times D \to \mathbb{R}^m and R:S1×D×(−ε0,ε0)→RmR:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m are piecewise Ck+1C^{k+1} functions and TT-periodic in the variable tt. Assuming that the unperturbed system x′=F0(t,x)x'=F_0(t,x) has a dd-dimensional submanifold of periodic solutions with d<md<m, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated TT-periodic solutions of the above differential system

    Characteristic ideals and Iwasawa theory

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    Let \L be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains \L_d and let MM be a finitely generated \L-module which is the inverse limit of \L_d-modules Md M_d\,. Under certain hypotheses on the rings \L_d and on the modules Md M_d\,, we define a pro-characteristic ideal for MM in \L, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a non-noetherian Iwasawa algebra \Z_p[[\Gal(\calf/F)]], where FF is a function field of characteristic pp and \Gal(\calf/F)\simeq\Z_p^\infty.Comment: 15 pages, substantial chenges in exposition, new section 2.

    Connexins: synthesis, post-translational modifications, and trafficking in health and disease

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    Connexins are tetraspan transmembrane proteins that form gap junctions and facilitate direct intercellular communication, a critical feature for the development, function, and homeostasis of tissues and organs. In addition, a growing number of gap junction-independent functions are being ascribed to these proteins. The connexin gene family is under extensive regulation at the transcriptional and post-transcriptional level, and undergoes numerous modifications at the protein level, including phosphorylation, which ultimately affects their trafficking, stability, and function. Here, we summarize these key regulatory events, with emphasis on how these affect connexin multifunctionality in health and disease

    On the expected number of perfect matchings in cubic planar graphs

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    A well-known conjecture by Lov\'asz and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other hand, Chudnovsky and Seymour (Combinatorica 2012) proved the conjecture in the special case of cubic planar graphs. In our work we consider random bridgeless cubic planar graphs with the uniform distribution on graphs with nn vertices. Under this model we show that the expected number of perfect matchings in labeled bridgeless cubic planar graphs is asymptotically cγnc\gamma^n, where c>0c>0 and γ∼1.14196\gamma \sim 1.14196 is an explicit algebraic number. We also compute the expected number of perfect matchings in (non necessarily bridgeless) cubic planar graphs and provide lower bounds for unlabeled graphs. Our starting point is a correspondence between counting perfect matchings in rooted cubic planar maps and the partition function of the Ising model in rooted triangulations.Comment: 19 pages, 4 figure

    Oscillatory and Fourier Integral operators with degenerate canonical relations

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    We mostly survey results concerning the L2L^2 boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.Comment: 37 pages, to appear in Publicacions Mathematiques (special issue, Proceedings of the 2000 El Escorial Conference in Harmonic Analysis and Partial Differential Equations

    Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis

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    We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age. The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. We then formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size: cells consume oxygen which in turns fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. This allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy

    Local positivity in terms of Newton-Okounkov bodies

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    In recent years, the study of Newton-Okounkov bodies on normal varieties has become a central subject in the asymptotic theory of linear series, after its introduction by Lazarsfeld-Mustata and Kaveh-Khovanskii. One reason for this is that they encode all numerical equivalence information of divisor classes (by work of Jow). At the same time, they can be seen as local positivity invariants, and K\"uronya-Lozovanu have studied them in depth from this point of view. We determine what information is encoded by the set of all Newton-Okounkov bodies of a big divisor with respect to flags centered at a fixed point of a surface, by showing that it determines and is determined by the numerical equivalence class of the divisor up to negative components in the Zariski decomposition that do not go through the fixed point.Comment: 10 pages. Comments welcom

    Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation

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    We investigate atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices in the limit of strong atom-atom interactions. We derive the effective Hamiltonian describing the dynamics of the system and discuss its low temperature physics. We demonstrate possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices.Comment: minor changes; Physical Review Letters 93, 040401 (2004

    Phase-dependent interaction in a 4-level atomic configuration

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    We study a four-level atomic scheme interacting with four lasers in a closed-loop configuration with a ♢\diamondsuit (diamond) geometry. We investigate the influence of the laser phases on the steady state. We show that, depending on the phases and the decay characteristic, the system can exhibit a variety of behaviors, including population inversion and complete depletion of an atomic state. We explain the phenomena in terms of multi-photon interference. We compare our results with the phase-dependent phenomena in the double-Λ\Lambda scheme, as studied in [Korsunsky and Kosachiov, Phys. Rev A {\bf 60}, 4996 (1999)]. This investigation may be useful for developing non-linear optical devices, and for the spectroscopy and laser-cooling of alkali-earth atoms.Comment: 4 figure

    Extracting Atoms on Demand with Lasers

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    We propose a scheme that allows to coherently extract cold atoms from a reservoir in a deterministic way. The transfer is achieved by means of radiation pulses coupling two atomic states which are object to different trapping conditions. A particular realization is proposed, where one state has zero magnetic moment and is confined by a dipole trap, whereas the other state with non-vanishing magnetic moment is confined by a steep microtrap potential. We show that in this setup a predetermined number of atoms can be transferred from a reservoir, a Bose-Einstein condensate, into the collective quantum state of the steep trap with high efficiency in the parameter regime of present experiments.Comment: 11 pages, 8 figure
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